How can I add Emission to the "Mortar" of a grid texture?
If you generate your grid texture with a Brick Texture node, you can connect the Fac output to the Emission Strength input of a Principled BSDF:

Note the green glow cast on the small sphere.
If you want a more visible glow/glare around the grid itself, you could try adding some volumetric mist, or you could fake it with Bloom (in Eevee) or using a Glare node in compositing (in Cycles). Here’s an example using Bloom:

(Note that to get the indirect lighting on the sphere to work in Eevee you will need to add Light Probes and bake the lights.)